Tianguang Chu

Bio: Tianguang Chu is an academic researcher from Peking University. The author has contributed to research in topics: Exponential stability & Swarm behaviour. The author has an hindex of 32, co-authored 122 publications receiving 3736 citations. Previous affiliations of Tianguang Chu include North China Electric Power University.

Controllability of a Leader–Follower Dynamic Network With Switching Topology

Abstract: This note studies the controllability of a leader-follower network of dynamic agents linked via neighbor rules. The leader is a particular agent acting as an external input to steer the other member agents. Based on switched control system theory, we derive a simple controllability condition for the network with switching topology, which indicates that the controllability of the whole network does not need to rely on that of the network for every specific topology. This merit provides convenience and flexibility in design and application of multiagent networks. For the fixed topology case, we show that the network is uncontrollable whenever the leader has an unbiased action on every member, regardless of the connectivity of the members themselves. This gives new insight into the relation between the controllability and the connectivity of the leader-follower network. We also give a formula for formation control of the network.

State Feedback Stabilization for Boolean Control Networks

Abstract: State feedback stabilization for Boolean control networks is investigated in this technical note. Based on the algebraic representation of logical dynamics in terms of the semi-tensor product of matrices, a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller, and a general control design approach is proposed when global stabilization is feasible via state feedback. Instead of designing the logical form of a stabilizing feedback law directly, we first construct its algebraic representation and then convert the algebraic representation back to the logical form. An example is worked out to illustrate the proposed design procedure.

Stabilization of networked control systems with data packet dropout and network delays via switching system approach

Abstract: An iterative approach is proposed to model networked control systems (NCSs) with arbitrary but finite data packet dropout. as switched linear systems. This enables us to apply the rich theory of switched systems to analyzing such NCSs. Sufficient conditions are presented on the stability and stabilization of NCSs with packet dropout and network delays. Stabilizing state/output feedback controllers can be constructed by using the feasible solutions of some linear matrix inequalities. The merit of the iterative approach is that the controllers can make full use of the previous information to stabilize NCSs when the current state measurements can not be transmitted by the network channel instantly. A simulation example is worked out to illustrate the effectiveness of the proposed approach.

An LMI approach to networked control systems with data packet dropout and transmission delays

Abstract: The problem of data packet dropout and transmission delays induced by communication channel in networked control systems (NCSs) in both continuous-time case and discrete-time case is studied in this paper. We model the NCSs with data packet dropout and delays as ordinary linear systems with input delays and this enables us to apply the rich theory of delay systems to analysis and design of such NCSs. For the continuous-time case, our technique is based on Lyapunov-Razumikhin function method. For the discrete-time case, we use the Lyapunov-Krasovskii based method. Attention is focused on the design of memoryless state feedback controllers that guarantee stability of the closed-loop systems. We present the admissible bounds of data packet loss and of delays in terms of linear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed approach.

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

A Survey of Recent Results in Networked Control Systems

Abstract: Networked control systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. We review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies

Controllability of complex networks

Abstract: The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system's entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network's degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the high-degree nodes.

Evolution and the Theory of Games

Abstract: In the Hamadryas baboon, males are substantially larger than females. A troop of baboons is subdivided into a number of ‘one-male groups’, consisting of one adult male and one or more females with their young. The male prevents any of ‘his’ females from moving too far from him. Kummer (1971) performed the following experiment. Two males, A and B, previously unknown to each other, were placed in a large enclosure. Male A was free to move about the enclosure, but male B was shut in a small cage, from which he could observe A but not interfere. A female, unknown to both males, was then placed in the enclosure. Within 20 minutes male A had persuaded the female to accept his ownership. Male B was then released into the open enclosure. Instead of challenging male A , B avoided any contact, accepting A’s ownership.

Linear systems

Abstract: Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge: